Question

if area of metallic wire becomes double and length is reduced to half its resistivity is?

Answer 1

Answer:

Resistance is directly proportional to area and inversely proportional to length.

Hence if we increase resistance we get increased area and decreased length and vice - versa.

Also Resistivity wont change if the length and area is changed. It remains constant for all values for a given material.

So,

Let the original length be = x  

Let the original area be = y

Resistivity = k ( Constant )

So Resistance = ky / x   -----( Equation 1 )

Now given that length is halved and area is doubled. Then we get,

Length = x / 2

Area = 2y

Resistivity = k ( Constant )

Now Resistance = k * 2y / x / 2

= 2 ky * 2 / x  

= 4 ky / x   -----( Equation 2 )

Now comparing Equation 1 and 2 we get that,

Resistance has become 4 times after modifications.

Hence Resistance will become 4 times in the new condition, if the area is doubled and length is halved.